60. Permutation Sequence

Author: coderbean

markdown/60. Permutation Sequence.md

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+### [60\. Permutation Sequence](https://leetcode.com/problems/permutation-sequence/)
+
+Difficulty: **Medium**
+
+
+The set `[1,2,3,...,_n_]` contains a total of _n_! unique permutations.
+
+By listing and labeling all of the permutations in order, we get the following sequence for _n_ = 3:
+
+1.  `"123"`
+2.  `"132"`
+3.  `"213"`
+4.  `"231"`
+5.  `"312"`
+6.  `"321"`
+
+Given _n_ and _k_, return the _k_<sup>th</sup> permutation sequence.
+
+**Note:**
+
+*   Given _n_ will be between 1 and 9 inclusive.
+*   Given _k_ will be between 1 and _n_! inclusive.
+
+**Example 1:**
+
+```
+Input: n = 3, k = 3
+Output: "213"
+```
+
+**Example 2:**
+
+```
+Input: n = 4, k = 9
+Output: "2314"
+```
+
+
+#### Solution
+
+Language: **Java**
+
+```java
+class Solution {
+    public String getPermutation(int n, int k) {
+        int[] factorial = new int[n + 1];
+        List<Integer> leftNumList = new ArrayList<>();
+        int sum = 1;
+        factorial[0] = 1;
+        for (int i = 1; i <= n; i++) {
+            leftNumList.add(i);
+            sum *= i;
+            factorial[i] = sum;
+        }
+        StringBuilder stringBuilder = new StringBuilder();
+        k--; // Amazing k--
+        for (int i = 1; i <= n; i++) {
+            int index = k / factorial[n - i];
+            k = k % factorial[n - i];
+            stringBuilder.append(leftNumList.get(index));
+            leftNumList.remove(index);
+        }
+        return stringBuilder.toString();
+    }
+}
+```
+![](http://ww1.sinaimg.cn/large/006tNc79gy1g4zps9z05tj31b40rwjwa.jpg)

src/main/java/leetcode/_60_/Main.java

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+package leetcode._60_;
+
+/**
+ * Created by zhangbo54 on 2019-03-04.
+ */
+public class Main {
+    public static void main(String[] args) {
+        Solution solution = new Solution();
+        System.out.println(solution.getPermutation(3, 3));
+        System.out.println(solution.getPermutation(4, 9));
+        System.out.println(solution.getPermutation(3, 1));
+    }
+}
+

src/main/java/leetcode/_60_/Solution.java

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+package leetcode._60_;
+
+import java.util.ArrayList;
+import java.util.List;
+
+class Solution {
+    public String getPermutation(int n, int k) {
+        int[] factorial = new int[n + 1];
+        List<Integer> leftNumList = new ArrayList<>();
+        int sum = 1;
+        factorial[0] = 1;
+        for (int i = 1; i <= n; i++) {
+            leftNumList.add(i);
+            sum *= i;
+            factorial[i] = sum;
+        }
+        StringBuilder stringBuilder = new StringBuilder();
+        k--; // Amazing k--
+        for (int i = 1; i <= n; i++) {
+            int index = k / factorial[n - i];
+            k = k % factorial[n - i];
+            stringBuilder.append(leftNumList.get(index));
+            leftNumList.remove(index);
+        }
+        return stringBuilder.toString();
+    }
+}

src/main/java/leetcode/_60_/solution.md

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+### [60\. Permutation Sequence](https://leetcode.com/problems/permutation-sequence/)
+
+Difficulty: **Medium**
+
+
+The set `[1,2,3,...,_n_]` contains a total of _n_! unique permutations.
+
+By listing and labeling all of the permutations in order, we get the following sequence for _n_ = 3:
+
+1.  `"123"`
+2.  `"132"`
+3.  `"213"`
+4.  `"231"`
+5.  `"312"`
+6.  `"321"`
+
+Given _n_ and _k_, return the _k_<sup>th</sup> permutation sequence.
+
+**Note:**
+
+*   Given _n_ will be between 1 and 9 inclusive.
+*   Given _k_ will be between 1 and _n_! inclusive.
+
+**Example 1:**
+
+```
+Input: n = 3, k = 3
+Output: "213"
+```
+
+**Example 2:**
+
+```
+Input: n = 4, k = 9
+Output: "2314"
+```
+
+
+#### Solution
+
+Language: **Java**
+
+```java
+class Solution {
+    public String getPermutation(int n, int k) {
+        int[] factorial = new int[n + 1];
+        List<Integer> leftNumList = new ArrayList<>();
+        int sum = 1;
+        factorial[0] = 1;
+        for (int i = 1; i <= n; i++) {
+            leftNumList.add(i);
+            sum *= i;
+            factorial[i] = sum;
+        }
+        StringBuilder stringBuilder = new StringBuilder();
+        k--; // Amazing k--
+        for (int i = 1; i <= n; i++) {
+            int index = k / factorial[n - i];
+            k = k % factorial[n - i];
+            stringBuilder.append(leftNumList.get(index));
+            leftNumList.remove(index);
+        }
+        return stringBuilder.toString();
+    }
+}
+```
+![](http://ww1.sinaimg.cn/large/006tNc79gy1g4zps9z05tj31b40rwjwa.jpg)